Nonexistence and multiplicity of positive solutions for an equation with degenerate nonlocal diffusion

We study the existence, nonexistence and multiplicity of positive solutions for a general class of degenerate nonlocal problems. The nonexistence results are provided in two different situations: under monotonicity assumptions involving the nonlinearity and without monotonicity conditions. A multipl...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2020-06, Vol.52 (3), p.489-497
Main Authors: Gasiński, Leszek, Santos, João R.
Format: Article
Language:English
Subjects:
35J20
35J25
35Q74 (primary)
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Summary:We study the existence, nonexistence and multiplicity of positive solutions for a general class of degenerate nonlocal problems. The nonexistence results are provided in two different situations: under monotonicity assumptions involving the nonlinearity and without monotonicity conditions. A multiplicity result of positive solutions with ordered Lp‐norms complement some recent results obtained in the Literature. Examples are provided in order to illustrate the applicability of our theorems.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12342